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The Gross–Pitaevskii hierarchy on general rectangular Tori
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Herr, Sebastian and Sohinger, Vedran (2016) The Gross–Pitaevskii hierarchy on general rectangular Tori. Archive for Rational Mechanics and Analysis, 220 (3). pp. 1119-1158. doi:10.1007/s00205-015-0950-2 ISSN 0003-9527.
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Official URL: http://dx.doi.org/10.1007/s00205-015-0950-2
Abstract
In this work, we study the Gross–Pitaevskii hierarchy on general—rational and irrational—rectangular tori of dimensions two and three. This is a system of infinitely many linear partial differential equations which arises in the rigorous derivation of the nonlinear Schrödinger equation. We prove a conditional uniqueness result for the hierarchy. In two dimensions, this result allows us to obtain a rigorous derivation of the defocusing cubic nonlinear Schrödinger equation from the dynamics of many-body quantum systems. On irrational tori, this question was posed as an open problem in the previous work of Kirkpatrick, Schlein, and Staffilani.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Archive for Rational Mechanics and Analysis | ||||||||
Publisher: | Springer | ||||||||
ISSN: | 0003-9527 | ||||||||
Official Date: | June 2016 | ||||||||
Dates: |
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Volume: | 220 | ||||||||
Number: | 3 | ||||||||
Page Range: | pp. 1119-1158 | ||||||||
DOI: | 10.1007/s00205-015-0950-2 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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